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Title: Mutually unbiased bases in six dimensions: The four most distant bases
Authors: Raynal, P. 
Lü, X.
Englert, B.-G. 
Issue Date: 6-Jun-2011
Citation: Raynal, P., Lü, X., Englert, B.-G. (2011-06-06). Mutually unbiased bases in six dimensions: The four most distant bases. Physical Review A - Atomic, Molecular, and Optical Physics 83 (6) : -. ScholarBank@NUS Repository.
Abstract: We consider the average distance between four bases in six dimensions. The distance between two orthonormal bases vanishes when the bases are the same, and the distance reaches its maximal value of unity when the bases are unbiased. We perform a numerical search for the maximum average distance and find it to be strictly smaller than unity. This is strong evidence that no four mutually unbiased bases exist in six dimensions. We also provide a two-parameter family of three bases which, together with the canonical basis, reach the numerically found maximum of the average distance, and we conduct a detailed study of the structure of the extremal set of bases. © 2011 American Physical Society.
Source Title: Physical Review A - Atomic, Molecular, and Optical Physics
ISSN: 10502947
DOI: 10.1103/PhysRevA.83.062303
Appears in Collections:Staff Publications

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